Introduction: The law of Zipf-Mandelbrot is a power law, which has been observed in natural languages. A mathematical diagnosis of fetal cardiac dynamics has been developed with this law. Objective: To develop a methodology for diagnostic aid to assess the degree of complexity of adult cardiac dynamics by Zipf-Mandelbrot law. Methodology: A mathematical induction was done for this; two groups of Holter recordings were selected: 11 with normal diagnosis and 11 with acute disease of each group, one Holter of each group was chosen for the induction, the law of ZipfMandelbrot was applied to evaluate the degree of complexity of each Holter, searching similarities or differences between the dynamics. A blind study was done with 20 Holters calculating sensitivity, specificity and the coefficient kappa. Results: The complexity grade of a normal cardiac dynamics varied between 0.9483 and 0.7046, and for an acute dynamic between 0.6707 and 0.4228. Conclusions: A new physical mathematical methodology for diagnostic aid was developed; it showed that the degree of complexity of normal cardiac dynamics was higher than those with acute disease, showing quantitatively how cardiac dynamics can evolve to acute state.
<p>Background. An exponential law for chaotic cardiac dynamics,<br />found previously, allows the quantification of the differences<br />between normal cardiac dynamics and those with acute<br />diseases, as well as the cardiac dynamics of the evolution<br />between these states.</p><p><br />Objective. To confirm the clinical applicability of the developed<br />methodology through the mathematical law for cardiac<br />dynamics in dynamics with arrhythmias.</p><p><br />Materials and methods. 60 Holter electrocardiograms were<br />analyzed, 10 corresponded to normal subjects, and 50 to subjects with different arrhythmias. For each Holter, an attractor was performed, and its fractal dimension and spatial occupancy were measured. A mathematical evaluation was applied in order to differentiate normal dynamics from pathological ones. Sensitivity, specificity and the Kappa coefficient were calculated.</p><p><br />Results. The mathematical evaluation differentiated occupation spaces, normal dynamics, acute illness dynamics, and evolution between these states. The sensitivity and specificity values were 100%, and the Kappa coefficient was 1.</p><p>Conclusions. The clinical applicability of the methodology<br />for cases with arrhythmia was shown. It is also applicable for<br />the detection of changes in dynamics that are not classified<br />clinically as pathological.</p>
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